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Make sure you're plugged into power and on WiFi before you start anything, because a failed transfer halfway through is a pain to recover from. The iCloud route works well for most stuff, but if you've got a ton of photos or videos, the phone-to-phone transfer via cable is faster and more reliable than waiting for cloud sync. Just don't close out of the setup process early thinking it's done - let it sit and finish completely, even if it looks stuck for a bit.
Use iCloud backup on your old phone, then restore it on the new one during setup - it's the most straightforward method and catches basically everything. If you want to be extra cautious, you could also plug both phones into a computer and use Finder (Mac) or iTunes (Windows) to verify the transfer went through, since I've seen the occasional hiccup with wireless transfers.
Quick restore during setup works fine for most people, but honestly the iCloud method others mentioned has one gotcha - if your backup is huge (like over 100GB), it'll take forever and might timeout. Direct transfer via cable or Wi-Fi migration (hold both phones together at setup) is way faster and more reliable, then sync any stragglers through iCloud afterward if needed.
The thing everyone forgets is to manually sign into your apps after the transfer instead of relying on auto-login - sounds tedious but it catches password changes and two-factor issues before they wreck your day! Also, if you've got a ton of photos or videos, do a wired transfer using a Mac or PC first, then sync the rest over iCloud, way faster than waiting for it all to upload and download again.
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